Closing the memory gap in stochastic functional differential equations

In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory

A Closer Look at Relationship Structures: Relationship Satisfaction and Attachment Among People Who Practice Hierarchical and Non-Hierarchical Polyamory

Although polyamorous relationships have received increasing attention from researchers over the past decade, little attention has been paid to differences in relationship configurations: some individuals arrange their relationships hierarchically, prioritizing a primary partner; other relationship structures are non-hierarchical with no relationships prioritized over others. Across two samples (NStudy1= 225; NStudy2= 360), we compared relationship satisfaction and attachment security between individuals in hierarchical and non-hierarchical configurations. Greater variability in attachment security was found between partners in hierarchical relationships than those in non-hierarchical relationships; no significant differences were found in variability in relationships satisfaction across these groups. Furthermore, individuals in hierarchical relationships reported lower overall relationship satisfaction and attachment security compared to individuals in non-hierarchical relationships. More specifically, although no significant differences were found between non-hierarchical and primary partners, participants reported lower relationship satisfaction and attachment security with secondary and tertiary partners compared to non-hierarchical and primary partners. Findings suggest that these differences may attenuate with time. Although previous research has found that differences (e.g., in investment) between partners exist in both non-hierarchical and hierarchical configurations, the current research suggests that differences that occur organically rather than in a predetermined manner may be related to greater similarities in attachment security across partners as well as greater overall levels of relationship satisfaction and attachment security for individuals in non-hierarchical configurations. More research is needed to determine whether the observed between-partner differences are consistent with the relationship goals of individuals in hierarchical relationships